Optical Zoom and Focal Length

Q: Most point & digital cameras come with lenses that are 3x, 10x, 12x, etc., but most SLR cameras use telephoto lenses that are 100mm, 300mm, etc. What is the relationship between the two systems? In other words, a 12x digital point and shoot equals what in a telephoto SLR lens? What is the conversion factor?

A: Point & shoot digital cameras have 35mm equivalencies, but they cannot be derived from knowing just the optical zoom because every model can be unique. For example, each digital camera model below is listed with its maximum optical zoom and corresponding 35mm equivalency zoom range (focal lengths) provided by the manufacturer:

Canon PowerShot SX10: 20x Optical Zoom / 28 - 560 mm

Sony Cyber-shot DSC-H20: 10x Optical zoom / 38 - 380mm

Nikon Coolpix 8400: 3.5x Optical Zoom / 24 - 85mm

Nikon Coolpix P5000: 3.5x Optical Zoom / 36 - 126mm

Notice that each camera has a different 35mm equivalency at 1x optical zoom. The two Nikon cameras have the same optical zoom (3.5x), but different 35mm equivalencies. This is because digital camera manufacturers can put whatever configuration of lens elements they want into an optical zoom system and won't necessarily render the same 35mm equivalency. However, the optical zoom can be computed by dividing the maximum 35mm equivalency focal length by the minimum:

560mm / 28mm = 20x

380mm / 38mm = 10x

85mm / 24mm = 3.5x

126mm / 36mm = 3.5x

And that's where the optical zoom number comes from! Optical zoom is only regarded as magnification in the sense how many times the minimum focal length in 35mm equivalency is being multiplied. If you want to calculate true magnification, simply divided focal length by 50 (from 50mm = 1x in 35mm equivalency).